Nonnegative doubly periodic solutions for nonlinear telegraph system

Journal of Mathematical Analysis and Applications

Volumn 338, Issue 1, 2008, Pages 91-100

  Wang, Fanglei ^a   An, Yukun ^a  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

Author keywords

Cone; Doubly periodic solution; Fixed point theorem; Telegraph system

Indexed keywords

EID: 34548814429     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.05.008     Document Type: Article

References (16)

1. Fucik S., and Mawhin J. Generated periodic solution of nonlinear telegraph equation. Nonlinear Anal. 2 (1978) 609-617
2. Kim W.S. Doubly-periodic boundary value problem for nonlinear dissipative hyperbolic equations. J. Math. Appl. 145 (1990) 1-6
3. Kim W.S. Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations. J. Math. Anal. Appl. 197 (1996) 735-748
4. Mawhin J. Periodic solution of nonlinear telegraph equations. In: Bedlarek A.R., and Cesari L. (Eds). Dynamical Systems (1977), Academic Press, New York
5. Ortega R., and Robles-Perez A.M. A maximum principle for periodic solutions of the telegraph equations. J. Math. Anal. Appl. 221 (1998) 625-651
6. Mawhin J., Ortega R., and Robles-Perez A.M. A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings. J. Math. Anal. Appl. 251 (2000) 695-709
7. Mawhin J., Ortega R., and Robles-Perez A.M. Maximum principles for bounded solutions of the telegraph equation in space dimensions two or three and applications. J. Differential Equations 208 (2005) 42-63
8. Li Y. Positive doubly periodic solutions of nonlinear telegraph equations. Nonlinear Anal. 55 (2003) 245-254
9. Li Y. Maximum principles and method of upper and lower solutions for time-periodic problems of the telegraph equations. J. Math. Anal. Appl. 327 (2007) 997-1009
10. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, New York
11. Berkovits J. On the Leray-Schauder formula and bifurcation. J. Differential Equations 173 (2001) 451-469
12. Berkovits J., and Mustonuen V. On nonresonance for system of semilinear wave equations. Nonlinear Anal. 29 6 (1997) 627-638
13. An Y. Periodic solutions of telegraph-wave coupled system at nonresonance. Nonlinear Anal. 46 (2001) 525-533
14. Dunninger D.R., and Wang H. Existence and multiplicity of positive solutions for elliptic systems. Nonlinear Anal. 29 (1997) 1051-1060
15. Zhou Y., and Xu Y. Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations. J. Math. Anal. Appl. 320 (2006) 578-590
16. Cheng X., and Zhong C. Existence of positive solutions for a second-order ordinary differential systems. J. Math. Anal. Appl. 312 (2005) 14-23